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Coloring maps 2 (1)

To force the use of 6 colors we do not need 32 regions, since 8 suffice:

Analogously, here is a sequence that shows how seven colors are needed to color a map with 10 regions:

Which is the minimal number of regions in a map that needs 8 colors to be colored incrementally? Is there a general formula or a general map structure that answers this question?